Goodness of fit measures

GARCH Models in Python

Chelsea Yang

Data Science Instructor

Goodness of fit

Can model do a good job explaining the data?

  1. Maximum likelihood
  2. Information criteria
GARCH Models in Python

Maximum likelihood

  • Maximize the probability of getting the data observed under the assumed model
  • Prefer models with larger likelihood values
GARCH Models in Python

Log-likelihood in Python

  • Typically used in log form: log-likelihood

Likelihodd example

print(gm_result.loglikelihood)
GARCH Models in Python

Overfitting

  • Fit in-sample data well, but perform poorly on out-out-sample predictions
  • Usually due to the model is overly complex
GARCH Models in Python

Information criteria

  • Measure the trade-off between goodness of fit and model complexity

  • Likelihood + penalty for model complexity

  • AIC: Akaike's Information Criterion

  • BIC: Bayesian Information Criterion

_Prefer models with the lower information criterion score _

GARCH Models in Python

AIC vs. BIC

  • Generally they agree with each other
  • BIC penalizes model complexity more severely
GARCH Models in Python

AIC/BIC in Python

AIC/BIC example

print(gm_result.aic)
print(gm_result.bic)
GARCH Models in Python

Let's practice!

GARCH Models in Python

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